Extended farewell for band on radio (4,4)

I believe the answer is:

long wave

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'radio' is the definition.
Both the answer and definition are singular nouns.
Maybe they are linked in a way I don't understand?

'extended farewell for band on' is the wordplay.
'extended' becomes 'long' (extended can mean longer than usual).
'farewell for band' becomes 'wave' (I can't justify this - if you can you should believe this answer much more).
'on' says to put letters next to each other.
'long'+'wave'='LONG-WAVE'

Can you help me to learn more?

(Another definition for long wave that I've seen is " Measuring over 1,000 metres (radio)".)

I've seen this clue in The Guardian.

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